Unstructured CFD for Wind Turbine Analysis C. Eric Lynch and Marilyn Smith Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta, USA
Wind availability: Egypt Extremely high wind availability on Red Sea coast Good to moderate wind availability in other portions
Wind Turbine Aeromechanics Siting, approximate models Elastic deformation Yaw error Atmospheric boundary layer Interactions Unsteady, separated flow Full configuration Horns Rev offshore wind farm, Denmark
Numerical Advances
Euler/Navier-Stokes Formulations Major goal of Euler/Navier-Stokes methods was ability to capture nonlinear effects without resorting to lower-fidelity methods that need empirical models Formulations include structured and unstructured, overset, chimera, etc., most typically finite-volume or finite-difference Dissipation of the wake vorticity remains biggest issue in long-age wake problems Grids too large for engineering applications Restrictive computational requirements Other research areas: Turbulence modeling Transition from laminar to turbulent flows
Emerging Technologies Reduced Unsteady Blade Models Intelligent Algorithms for CFD Spatial and Temporal Multi-scales Improved Hybrid Methods to Resolve the Far Wake: Cartesian CFD with Grid Adaptation/Refinement Vorticity Transport Methods Vorticity Confinement Methods Vortex Element Methods
CFD Methods National Research Codes e.g., OVERFLOW, FUN3D Pro: CS supported, many features, source code, no cost Con: Access by US citizens only Commercial Codes e.g., FLUENT, CFD++ Pro: Access by everyone, CS supported, many features Con: Executables only, pay to use, highly dissipative to improve code robustness International Research Code OpenFOAM Pro: Access by everyone, many developers support, no cost Con: Not as many features as other two categories
Prior CFD Efforts Hybrid RANS-VE method for single blade (Sankar et al.) Incompressible, non-inertial (Sorensen et al. 2002) Pinpointing of separation as source of unsteadiness (Le Pape and Lecanu 2004) Structured overset (Duque 1999) Comparison of structured overset with comprehensive analysis (Duque 2003) Time-accurate overset incompressible with tower (Zahle 2004, 2007) Unstructured non-inertial with grid adaptation (Potsdam, 2009)
L Importance of Turbulence modeling RANS 100% l Eddies with Energy RANS VLES Inertial Subrange Hybrid RANS-LES LES η Turbulence Scales Viscous Range Experiment 1 1 Wilcox, D. C., Turbulence Modeling for CFD, DCW Ind., 2004 DNS 0% Statistical Modeling of Turbulence
Hybrid RANS/LES Use RANS near the wall where finest grids are required Use LES away from wall to model largest turbulent eddies Detached Eddy Simulation (DES) is a common form of hybrid model Georgia Tech HRLES-sgs model: RANS based on Menter s k-ω SST, solving for turbulent kinetic energy and dissipation LES based on Menon and Kim constant coefficient k-δ model Two sets of equations are linearly blended using a blending function RANS HRLES-sgs shown to capture more physics and provide better performance predictions even on RANS mesh sizes LES
HRLES-sgs versus RANS SST HRLES
Flatback airfoil test case Attempt to emulate wind tunnel tests of Berg and Zayas (2008) DU97 flatback airfoil with 10% thick trailing edge Wind tunnel wall porous effects not known Compressible, M = 0.2 Re = 3 x 10 6 α = 10 o Δt = 0.005, ~ 500 steps/cycle
Computational Grids Results vary significantly with grid topology/resolution: 1. Prismatic with tunnel walls, 5h/33, 108k nodes per plane, periodic BC 2. Hex overset with farfield boundaries, 5h/33, 7.2M nodes
Prisma'c, w/ tunnel walls, periodic BC in spanwise dir. Vortex shedding: Q criterion SST HRLES Hex grid, overset, farfield BCs
Mean forces and Strouhal number Grid Model Code Mean CL Mean CD Strouhal Experiment 1.57 ± 0.13 0.055 ± 0.005 0.24 ± 0.01 Prisma'c with walls SST FUN 1.87 0.0493 0.088 HRLES FUN 1.88 0.0740 0.088, 0.15 Hex overset, farfield SST FUN 1.615 0.039 0.177 HRLES FUN 1.647 0.061 0.182
NREL Phase VI cases 7, 13, and 15 m/s upwind baseline cases at zero yaw Compared against Sequence S (no probes, free transition) and Sequence M (no probes, tripped) Found very few transitional effects, so only untripped results shown here
Full Wind Turbine Grids 2.6M nodes per blade volume grid 129k surface triangles per blade 7.2M total
Integrated loads Wind speed (m/s) Code Turb. model Root flap bending moment (N m) Torque (N m) 15 Exp. S 2750 ± 260 1172 ± 95 FUN3D SST 3067 922 FUN3D HRLES 2898 646 OF SST 2789 988 Unstructured method captures root bending moment within experimental limits Low torque predictions common to structured mesh as well Blade tip modeling inconsistencies were observed. OVERFLOW results courtesy of Dr. Chris Stone, Computa(onal Science, LLC
Instantaneous streamlines 30% span 47% span 63% span 80% span 95% span SST HRLES Instantaneous streamlines at 0 degrees azimuth
Rotor near wake: Q criterion k-w SST HRLES Q = 1 x 10-4 iso-surfaces, colored by vorticity magnitude, after 5 revs
Blade Pressure Distributions Cp at 30% span Cp at 95% span Well within experimental error bars near root. Less so at tip where grid problems are most pronounced
Actuator Methods A compromise between full rotor CFD and lower fidelity methods Based on momentum theory Remove the rotor and model its influence on the flow field Can be implemented as a pressure discontinuity BC or as body forces (source terms) in interior Efficient because need not model blade geometry or boundary layers
Actuator blades/lines Locate sources along lines or moving surfaces Source strength comes from BEM or comprehensive methods Actuator disc Actuator blades
Actuator blade improvements Sources must be associated with a grid node, entailing a search at each time step recent work increases search speed by 20% Coupling with DYMORE to use its finite-state aerodynamics model to determine source strengths with azimuth T. Renaud, M. Potsdam, D. M. O Brien, Jr., and M. J. Smith, Evaluation of Isolated Fuselage and Rotor- Fuselage Interaction Using CFD, 60th AHS Annual Forum, Baltimore, MD, June 2004.
Current & Future work Improve quality of surface definition Evaluate sensitivity to grid quality and spacing Transition model for critical speed (10m/s) Yawed cases to better demonstrate advantages of full configuration CFD Use incompressible method to avoid low Mach converge and accuracy problems CFD-CSD coupling to capture blade flexibility Addition of atmospheric boundary layer model
Conclusions Hybrid turbulence models improve sectional loads and surface pressures in separated regions With HRLES, more of the unsteady wake physics is observed in the rotor wake Grids cannot be readily used from their structured counterparts as they can result in poor unstructured meshes Actuator blades hold promise to model wind farms by capturing individual rotor wakes
Acknowledgments Work supported by NSF Project 0731034, Advancing Wind Turbine Analysis and Design for Sustainable Energy Teragrid computing resources hosted at NCSA, Purdue, and LONI were used Thanks to Scott Schreck for the NREL Phase VI datasets